Simplify. Multiply and remove all perfect squares from inside the square roots. Assume $x$ is positive. $\sqrt{3x^4}\cdot\sqrt{5x^2}\cdot\sqrt{10}=$
Solution: Let's start by merging the square roots: $\begin{aligned} \sqrt{3x^4}\cdot\sqrt{5x^2}\cdot\sqrt{10} &=\sqrt{3x^4\cdot 5x^2\cdot 10} \\\\ &=\sqrt{150x^6} \end{aligned}$ Now we remove all perfect squares from inside the square root: $\begin{aligned} \sqrt{150x^6} &=\sqrt{5^2\cdot 2\cdot 3\cdot \left(x^3\right)^2} \\\\ &=\sqrt{5^2}\cdot\sqrt{6}\cdot\sqrt{ \left(x^3\right)^2} \\\\ &=5\cdot \sqrt{6}\cdot x^3 \\\\ &=5x^3\sqrt{6} \end{aligned}$ In conclusion, $\sqrt{3x^4}\cdot\sqrt{5x^2}\cdot\sqrt{10}=5x^3\sqrt{6}$